Why do people feel the need to shout into the phone?
The other end of the phone call is worth noting here. If it is in a loud environment then there may be the need to raise one's voice. If one is doing negotiations and wants to convey firmness, one may increase the volume in their voice to do this. However, these require one to know the full context which if you think shouting is never OK over the phone, I doubt you've seen these situations. Perhaps the other end has a hearing difficulty and asks the person to speak up on the phone so that to others this is shouting.
The phone transmits your little voice long distances, that's kind of
it's main function. Is there a non-confrontational way that I can
manage this problem?
Other than tuning it out, not really as you don't know what is going on with the other end which is something to consider here.
I have tried being direct but it has no effect on behaviour after an
hour or so. Decibel meter by the phone maybe with an alarm that goes
Do you have the power to enforce a threshold of the limit and would this be the same all the time? Someone with sensitive hearing may consider something shouting that is merely assertive to someone else.